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This is set during the Renaissance, a mostly normal European setting.

Magic works through controlling the flux of energy. A mage can't simply create energy, but he can store and change it.

Most mages will meditate in front of water barrels, draining heat from the water until it turns into ice. A regular mage can generate about two barrels of ice per week.

Would this method be able to generate significant income for the mages?

Cyn
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Sasha
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    Heat does not move spontaneously from a cooler object to a warmer object. You need energy to pump it against a temperature gradient. – AlexP Mar 30 '18 at 04:46
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    @AlexP In this context, why would that have to be so? This is a magical system we're talking about. – AngelPray Mar 30 '18 at 06:34
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    @AngelPray: The question says that the mages can "control the flux of energy". It does not say anything about entropy, so the comment was a gentle reminder that in order to move heat from a cold system to a warm system without expending energy the mages need supplementary powers. – AlexP Mar 30 '18 at 07:31
  • @AlexP The energy could come out of the energy being moved itself. We can't do this using modern technology, but in theory it's possible. Supposing it were two barrels of water, rather than one becoming frozen and the other boiling, the latter would simply be lukewarm, having spent some of the energy in the transfer. – Neil Mar 30 '18 at 08:53
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    @Neil: In theory it's not possible, because it would break the second law of thermodynamics and allow the construction of a perpetual motion machine of the second kind. Breaking the second law of thermodynamics would allow for all sorts of wondrous effects, and is generally considered a massive departure from the word as we know it. It is really that easy: heat will not move spontaneously from a cooler system to a warmer system. Not all of it, not part of it, not a tiny little bit of it: none at all. – AlexP Mar 30 '18 at 10:29
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    @AlexP Nobody is talking about moving heat without expending energy. The energy comes from the heat itself being moved. The net temperature after transferring heat from one barrel of water to another would be less than room temperature (assuming barrels were insulated and didn't leak heat). – Neil Mar 30 '18 at 10:33
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    @Neil: You cannot cheat and say that you took 2 joules from the cold system and only one got to the warm system. You must put energy into the system from the ouside, because otherwise the net effect would be that heat moved spontaneously from cold to hot, which is forbidden. – AlexP Mar 30 '18 at 10:38
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    @AlexP Well making a barrel of water turn to ice without any otherwise mechanical interaction is precisely what we're talking about here. Presumably there is a certain level of "magic" going on that allows this to happen, otherwise what are we talking about? If this were possible in real life, we could all transform barrels of water to ice like mages. – Neil Mar 30 '18 at 11:35
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    @AlexP This happens because the "spirits" that mages use to store energy are considered to be about 0K in our world. The mage works as a conduit between these entities and our world, being able to channel energy between the two. – Sasha Mar 30 '18 at 13:08
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    Just a note for other answerers: Mages could effectively desalinate ocean water by freezing barrels of it – user70585 Mar 30 '18 at 19:29
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    I don't understand the premise of "2 barrels per week". Does the mage literally sit in front of each barrel for 3.5 days at a time without breaks? If not, wouldn't the water start heating up again whenever the mage took a break? Only 2 barrels a week seems incredibly low to me—that's a lot of work for very little gain. Why not something like 200 barrels per week or, say, a barrel per hour? Then the mage could probably earn a nice living. – user428517 Mar 30 '18 at 20:35
  • @sgroves Freezing a single barrel would take about 10 hours of meditation, but after that the mage needs to bleed out the energy before he can absorb anymore. Also, these mages need to take care of most domestic duties and conduct their own experiments. – Sasha Mar 30 '18 at 20:57
  • @Sasha Gotcha. That makes sense to me now. – user428517 Mar 30 '18 at 20:59
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    @AlexP the question is marked as magic and does not ask for the feasibility of the process... it just asks if this is a profitable endeavor for mages in this world – V. Sim Mar 31 '18 at 00:25
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    @AlexP When you find yourself arguing that magic doesn't follow scientific principles, its time to take a step back, take a break, something. Yeah, we know magic violates scientific principles, even the 2nd law. That's why it is magic. – Shane Apr 01 '18 at 01:40
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    @Shane: My initial comment was intended simply to stress that the power assigned to the mages by the inquirer was not enough for them to achieve the declared effect, and that for the effect to occur they need an unstated power, which is in actuality much more interesting. I did not question their magic abilities, only the inquirer's description. – AlexP Apr 01 '18 at 01:57
  • Perhaps mage-ice has the interesting property that when it "melts" it doesn't leave any water behind. And unlike water ice, mage-ice can BURN you!! And if you drop a piece into a drink, the drink bubbles and foams!!! Not even the mages know why, so...CALL FOR THE ALCHEMISTS!!!! (And for heaven's sake, make sure they don't blow themselves up...again...) – Bob Jarvis - Слава Україні Apr 02 '18 at 02:23

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There really wasn't an Industry for ice until 1805 when the first guy named Frederic Tudor tried to sell ice from new England in the Caribbean. Literally nobody wanted to buy it, and he spent 13 years trying to sell it and ended up in debtor's prison on 3 separate occasions trying to convince people that they even needed it. He was so obsessed with the idea of selling ice that he began bringing chilled beverages to entertain guests, who often scoffed at the idea of adding ice to a drink... until they tried it. He spent 20 years of aggressively marketing ice to people, convincing (even paying) bartenders to popularize chilled drinks, teaching vendors how to make and sell ice-cream, and convincing doctors it was required to cool down feverish patients. His idea FINALLY caught on around the mid 1820's and he ended up rich after two decades of introducing ice as a new cultural phenomenon.

The guy basically forced a meme in the age prior to internet. As odd as it sounds today up until that point people just really didn't care about drinking or eating cold stuff, there was somewhat a cottage industry in some cultures but it really wasn't something people wanted to pay for (packing root cellars with snow and such). Thing is, Ice as a product really didn't catch on in a big way until the 1840's, peaked in the 1860's, and was replaced by refrigeration in the 1900's. This all may seem like a distraction, but my point is people needed to be convinced they even wanted to pay for ice!

The average value of ice in the mid to late 1800's was 10 cents a pound, or about $2.70 cents today, ice vendors made their profits by selling anywhere from 10 to 50 tons of ice a season (with a total income per shipment of 54 thousand to 260 thousand dollars.) So a few barrels of ice a week wasn't worth much in the 1800's, (a few dollars) and wasn't really worth anything prior to the 1830's (nobody wanted it.)

But see, that's the REAL WORLD history of ice selling. You are writing a fictional world. So you got cash strapped mages who make ice as a byproduct of their work. So these mages decide to make up some snake oil, they start a rumor that "mage-ice" is super duper special compared to "normal ice." Chock full of good humors and invigorating spirits and what-not which are "rumored" to extend ones life, improve ones looks, and boost ones intelligence! (never mind the person who started those rumors is the ones selling the magic ice!) It becomes "fashionable" for Nobles to show off their clout by outbidding each-other and engaging in petty little squabbles to have a house mage on staff so they can have as much access to this wonderfully magical substance as possible. (in other words your mages do just what Frederic Tudor did in the 1820's and convince people its something they even really want to buy)

Brythan
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TCAT117
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    Creating a market ? Just advertise it as "better than Viagra". Success guaranteed. – Tonny Mar 30 '18 at 09:48
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    Sounds like the anti-malware market... ^^ It's all about the perceived need, and the perceived value. – nijineko Mar 30 '18 at 17:06
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    There really wasn't an Industry for ice until 1805. WRONG. Conservation of food has always been a use for ice, and certainly people did enjoy ice-cream and cold drinks. https://en.wikipedia.org/wiki/Ice_house_(building). A cuneiform tablet from c. **1780 BC** records the construction of an icehouse in the northern Mesopotamian town [...]. Certainly it was more limited due to technical issues, though. – SJuan76 Mar 30 '18 at 20:47
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    @SJuan76: Also was well known (if expensive) in ancient Rome. – jamesqf Mar 31 '18 at 03:14
  • Also, ice was used in the manufacture of beer long before the 1800's. – vsz Mar 31 '18 at 09:46
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    Theres a difference between something being used, and something being marketed. People USED ice for plenty, but nobody really felt it was a commodity worth purchasing regularly. A guy shoveling snow into his root cellar or a noble ordering his serfs/slaves/servants or whatever to build him an ice house is NOT the same as a commodity being sold and marketed. – TCAT117 Mar 31 '18 at 10:09
  • Note that that price makes a two barrels/week worth about $10k/week in today's money, so mages generate about a half-million dollars a year in today's dollars. (which you may want to add because it answer the actual question posed) – fectin Mar 31 '18 at 12:51
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    Ice had been marketed in large amounts in Southern Europe for centuries before 1830. Please see references in my answer. The fact that it was hard to sell shiploads of ice in the Caribbean by 1830 doesn't mind it wasn't expensive in other places before that time, even at a smaller scale. Furthermore, the productivity of the OP's magician should compare to places and times where ice was brought by cartloads more than shiploads. – Pere Mar 31 '18 at 19:38
  • @SJuan76 Note in hot coastal climates you can get salt instead of ice and it's cheaper and better to conserve meat – jean Apr 02 '18 at 12:25
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Would this method be able to generate signficant income for the mages?

Yes, it would. In a time when electric power was unknown, this would be the only viable way to have ice made easily available for many latitudes. The ice trade would start a few centuries earlier.

Ice created by magic would help preserve food anywhere in the world. Just this alone would be a major revolution. It would change the economy for food markets as well as for nautical exploration. Seriously, go read First Voyage Around the World by Antonio Pigafetta. After months onboard sailors would trade a king's ransom for a dead rat because it was the freshest edible thing available.

Ice has other uses as well. Medically, it can be used to treat rash and first degree burns, for example. Doctors would also use it to fight fevers. Barbers could press ice on a client's cheek after removing their teeth (barbers were the dentists of the past).

Gastronomically, asides preserving food, it is used in the making of ice cream. Ice cream is as old as the ancient romans, but you had to climb a mountain or wait for a snowy winter before the ice trade became a thing in the 19th century. If you think this is silly, remember that during the crusades people would kill for a pint of sugar.

People would find other creative uses for ice. If you want to take water upstairs, for example, you have to move the weight of the water + its container. With ice blocks, you don't necessarily need a container. And if you need to move heavy furniture around, perhaps placing it over a slab of ice makes things easier.

So long story short, I think not only the mages could make a living, they would be wealthy, upper class citizens.

The Square-Cube Law
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    I think anyone with the power to drain the heat from the body of an individual and killing them on a whim would find some way of staying on top of things for sure.. – Neil Mar 30 '18 at 08:57
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    The process of draining heat is slow and demands concentration, so you wouldn't be able to kill someone unless the person was tied and/or unconscious. Not really something you can use on a whim. – Sasha Mar 30 '18 at 12:46
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    Just a minor point of interest barbers were not just dentists but surgeons as well, Physicians did not perform surgical tasks. – Sarriesfan Mar 30 '18 at 15:14
  • @Sasha What if the object they are draining heat from is very small, say, roughly the size of a brainstem? – Vaelus Mar 30 '18 at 16:00
  • @Vaelus They still would need to spend a long time concentrating on the object and without being able to see the object they would have to estimate where it is. The process would probably still take a long time and you better hope your target isn't moving around. – Sasha Mar 30 '18 at 16:30
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    @Vaelus in this case, the mages are trying to prove they can work near other people, so going around killing people is not exactly in their best interest. – Sasha Mar 30 '18 at 16:35
  • Simply not true that it would be the only way to get ice, at least in Europe or places with a similar climate & geography. In fact, it wouldn't even be that profitable, as either cutting blocks from lakes and storing them in icehouses, or hauling wagon loads from the nearest mountain, would be considerably cheaper than using mages, who are presumably rather rare & sought after. – jamesqf Mar 31 '18 at 03:18
  • "And if you need to move heavy furniture around, perhaps placing it over a slab of ice makes things easier." wait what – Yakk Apr 02 '18 at 15:02
  • @Yakk ice tends to be slippery. – The Square-Cube Law Apr 02 '18 at 17:12
18

TL;DR

The magician can earn a living quite well by producing ice, but don't expect him to get very rich.

We don't need to speculate. Natural ice trade is widespread and very well documented in medieval and modern ages -at least in Southern Europe-, and we just need to check for ice price to see what is worth the ice the magician can produce.

According to this paper (in Catalan) the official price to sell ice to the public in Estanyó (near Girona in Catalonia) was 7.5 denier/kg (cheaper than wheat, bread or wine), and that was about 1/6 of the daily wage of an unskilled worker.

According to the OP, the magician can turn two barrels of water into ice per week, although we don't know how big are those barrels. Assuming they are 100 litres barrels, the magician is producing about 1500 deniers/week, or the equivalent to 32 unskilled worker daily wages per week. That is, the ice he produces in a day is worth the wages of 5 unskilled workers.

From this amount we should detract the costs of distribution and taxes, since somebody needs to cut and sell the ice and ice was a heavily taxed industry.

I just used data from one place, which was just a village not far from ice sources. Probably in large cities more distant from ice sources the magician could get a better rate.

Pere
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Anywhere there is a fishing industry will have a market for ice. So, large rivers, coastlines and islands. Ice gets its value there from preserving fish, allowing transport for a few days to markets inland.

In contrast to luxuries like cold drinks and ice cream, this puts it squarely into the realm of the essential - both for the inland city dweller whose life depends on adding protein to an otherwise poor diet, but also for the fisher people whose livelihood depends on getting their catch to market.

There's a distinct type of architecture known as an ice house, often built near the harbour pier in Scottish seaside villages.

enter image description here (image source)

You can push the timeline back a bit earlier than 1805 ... 1785 in Scotland, from a man who brought the idea of preserving ice home from travelling in China - you might follow it back to China to push the timeline back further still.

From the linked article:

At least 7,500 cartloads, or 2,000 tons of ice were needed to fill Berwick's ice-houses. During the 19th century, the ice needed was usually sourced from the River Tweed and harvested from ponds created in the district specially for the purpose, such as those at Heatherytops in Scremerston, about three miles south of Berwick. If sufficient amounts of ice could not be found locally, the Berwick Salmon Fisheries Company imported supplies from Norway. As early as 1833, there are records showing that ice was imported from Norway following a mild winter. The last ice-ship came to Berwick from Norway in 1939.

Having a local maker would be much more convenient than an international transport and storage system.

Ice houses quickly spread round the country from that first one, many still survive today though they fell into disuse when refrigeration came along.

The fact that custom buildings were worth building, insulated well enough to preserve winter ice through the summer, gives some idea of the real value of ice.

user_1818839
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Ice was extremely popular in Renaissance Italy. It was added to wine to cool it down, used to keep wine chilled, both in the wine cellar and in the cup. Eventually a cup designed to hold ice or snow while another cup of wine was placed on top. They also used ice and snow to keep fruit, juice and other refreshments cold.

Ice cream would be another source of income. In Florence ice cream and sorbets were refined and extremely popular amongst those who could afford it. It was also used for special events among the rich in France and several other Southern and Central European countries.

So yes, money could be made as long as the mage is in a warm place.

Dan Clarke
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Heck yeah! The ice trade didn't even begin until 1806. Before then, some ice (never large amounts) was captured from the Alps, etc., during the winter and stored (likely poorly) for summer use. Your mages would make a boat load during the summers (and not a penny during the winter), unless there are so many mages that it gluts the market.

Out of curiosity, though, why water? If the mages are drawing thermal energy from water, why not from fire, which is obviously more thermally dense? If you started with boiling water, the amount of energy drawn from two barrels to freeze them wouldn't be equal to draining a fire in a couple of minutes.

JBH
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    I do not think fire is obviously more thermally dense. Water has much higher density than the flames do. I think a few orders of magnitude higher, meanwhile the heat difference is only a factor of two or three. And uncontained gas will just expand as it is heated so the thermal density does not really go up that much, I think. Besides, focus on swirling gas is probably more difficult than focusing on a liquid. A solid object might actually be even easier? Just to be clear, I am not saying you are wrong on thermal density, just that it does not seem obvious to me. – Ville Niemi Mar 30 '18 at 05:16
  • They would use water for praticity, if you drain the energy from fire, then you will have ashes that will be worth nothing as the end result. – Sasha Mar 30 '18 at 12:49
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    @VilleNiemi, The reason it's obvious is because if a volume of water (way one cubic centimeter) had the same thermal density as a fire (say a candle flame, about one cubic centimeter) it would be flashing (flashing, not boiling) into steam. It might even be flashing into ionized gas. I'd have to run the numbers to be sure. – JBH Mar 30 '18 at 13:38
  • Sorry, I still do not see it. One cubic centimeter of water has much higher thermal mass than one cubic centimeter of flame does. so if with thermal density you mean thermal energy per volume it won't have much effect on the water. And it is not obvious to me what else you could mean. – Ville Niemi Mar 31 '18 at 12:22
  • @VilleNiemi The number of therms per cubic centimeter is higher for a combusting flame than for standing water. The mass of the medium is irrelevant (actually, it isn't. It's the problem. More stuff to heat = lower thermal density). – JBH Mar 31 '18 at 13:34
  • You are talking about the density of the thermal flow then? I can understand that as the question specifically talks about controlling the thermal flux in which case flame would indeed be better (and sunlight I guess even better as it is essentially free and unlimited?). But the question then talks about drawing thermal energy, in which case water would be better. Well, whatever, I now understand what you meant, so no reason to bug YOU with that ambiguity. – Ville Niemi Mar 31 '18 at 13:48
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Would this method be able to generate significant income for the mages? Yes if he uses his brain.

Most of the population during Renaissance didn't have to worry about storing food, as they barely had enough to consume each day.

Things change if your mage operates in the surroundings of a court. And I suppose he already does, following Merlin example at the court of King Arthur.

In the past snow was collected and stored in cellars, and its use was mostly dedicated to prepare sorbets and ice creams for the courts. Your mage can enter this business, actually getting appointed as "official sorbeteer of his highness the of ".

There he can also use ice to improve storage of food needed for the court, and even provide ice for the times when somebody gets ill or hurt.

The above also suggests that your mage can have better fortune (read less competition) in southern countries where harvesting natural snow is somehow more difficult.

L.Dutch
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In this time period, ice is likely going to be popular with the very rich for its rarity and its ability to preserve delicate foods so they can be eaten out of season, especially if wizards are rare enough that someone's only going to be able to buy a few dozen ice barrels at a time and if there aren't any nearby tall mountains for easily-accessible snow.

Back in Roman times, the super-rich would hire fast chariots to speed the asparagus harvest (early Spring) from the Tiber river high into the Alps so that the snows would preserve the asparagus until the feast of Epicurious in Fall, and they'd pay insane amounts for the service.

Carduus
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The availability of ice in the middle ages would have changed society out of recognition. Having refrigeration would mean that every foodstuff could be stored and eaten at any time of year. It would mean that humanity would not have depended on seasons. Almost all the great festivals we have are to do with seasons. True many of them stem from a long time before the renaissance, but they are gradually being ignored and forgotten. Perhaps we would not even notice the coming of spring if we had been living with fridges for hundreds of years.

Janet Rooke
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